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© 2014

Finite Sample Analysis in Quantum Estimation

Book

Part of the Springer Theses book series (Springer Theses)

Table of contents

About this book

Introduction

In this thesis, the author explains the background of problems in quantum estimation, the necessary conditions required for estimation precision benchmarks that are applicable and meaningful for evaluating data in quantum information experiments, and provides examples of such benchmarks.

The author develops mathematical methods in quantum estimation theory and analyzes the benchmarks in tests of Bell-type correlation and quantum tomography with those methods. Above all, a set of explicit formulae for evaluating the estimation precision in quantum tomography with finite data sets is derived, in contrast to the standard quantum estimation theory, which can deal only with infinite samples. This is the first result directly applicable to the evaluation of estimation errors in quantum tomography experiments, allowing experimentalists to guarantee estimation precision and verify quantitatively that their preparation is reliable.

Keywords

Finite Sample Analysis Quantum Estimation Theory Quantum Information Quantum Tomography Statistical Error Analysis Test of Bell-type Correlation

Authors and affiliations

  1. 1.Department of Physics Graduate School of ScienceThe University of TokyoTokyoJapan

About the authors

Dr. Takanori Sugiyama Department of Physics, Graduate School of Science, The University of Tokyo

Bibliographic information